Computational Fluid Mechanics (CFD) allows increasingly accurate and efficient simulations of complex fluid dynamic phenomena. In this entry we will discuss a family of particle-based numerical methods. Among these methods, the most common are Smooth Particle Hydrodynamics (SPH) and Moving Particle Semi-Implicit (MPS), which have proven to be especially effective in problems with free surfaces, such as waves, impacts and liquid spills. They are also useful for solving problems where there is fluid-structure interaction.
At ICEMM we have used this technology with the Particleworks software, which allows mesh-free simulations based on the MPS method to be carried out taking advantage of the computing power of GPUs.
What are particle methods in CFD?
Particle methods present an alternative mathematical formulation to traditional CFD solving schemes such as the finite volume method (FVM) or the finite element method (FEM).
With particle methods, the fluid domain is not represented by a grid. Instead, a set of discrete particles carrying the physical properties of interest is used.
The mathematical formulation of these methods is based on the Lagrangian description of the flow. Roughly speaking, this means that the equations are formulated following the motion of the flowing particles, treating them as material points containing both the mass and the intensive properties under study.
In the absence of a mesh, the interpolation used for the numerical method is based on a weight function, usually called ‘Kernel’. This represents the influence of some particles on others according to the distance between them. It is used to define the influence and interaction of particles with each other and thus study the evolution of their properties. A common type of kernel function is shown in the picture below:
These methods are able to represent flows in very complex situations and geometries. However, their use presents some challenges, such as numerical stability in compressible flow scenarios, the treatment of surface tension in detailed simulations or ensuring conservation properties.
In which cases are particle methods useful compared to finite volume methods?
Although mesh-based methods, and especially the finite volume method, are widely used in industry, particle-based methods have some key advantages in certain applications:
- Flows with free surface: In cases where the flow has fast motions, the Lagrangian formulation avoids the need to follow the interface. In particular, particle methods make it easier to represent the interactions of small amounts of liquid with solid surfaces or other fluids.
- Lubrication and cooling systems: These methods allow for a more natural representation in highly dynamic fluid scenarios, such as industrial machinery or engines.
- Flows with complex geometries: These schemes are able to adapt to deformable or moving structures without requiring constant remeshing, which also has an impact on computational efficiency.
Use cases at ICEMM
Particle methods are very useful for the simulation of free surface flows and complex fluid dynamic phenomena. There are now also commercial tools such as Particleworks that offer the possibility of combining particle methods with conventional finite volume schemes, or even Lattice-Boltzmann methods. In this way, the advantages of both approaches can be exploited depending on the case of study.
Here are a couple of examples we have studied at ICEMM using particle methods in CFD simulations.
First, we analyse the flow in an open channel, where we study the velocities and the possible occurrence of overflows in the face of design obstacles:
Secondly, we show a case we have already analysed with the FVM where we simulated a deflector system for a water jump. Here we perform the study using particle methods:
